Mathematical Proof The Eagle In The USPS Logo Is FAST!

The logo for the United States Postal Service is a mean-looking eagle. But a true fluid dynamics geek might look at it and realize that eagle is moving so fast it’s causing a shock wave. But just how fast is it moving? [Andrew Higgins] asked and answered this question, posting his analysis of the logo’s supersonic travel. He claims it’s Mach 4.9, but, how do we know? Science!

It turns out if something is going fast enough, you can tell just how fast with a simple picture! We’ve all seen pictures of jets breaking the sound barrier, this gives us information about the jet’s speed.

Mach Lines

How does it work?

Think about it like this: sound moves at roughly 330 m/s on Earth at sea level. If an object moves through air at that velocity, the air disturbances are transmitted as sound waves. If it’s moving faster than sound, those waves get distributed downstream, behind the moving object. The distance of these waves behind the moving object is dependent on the object’s speed.

This creates a line of these interactions known as a “Mach line.” Find the angle difference of the Mach line and the direction of travel and you have the “Mach angle” (denoted by α or µ).

There is a simple formula for determining the speed of an object using the Mach angle, the speed of sound (a), and an object’s velocity (v): sin(µ) = a / v.  The ratio of to a is known as the Mach number, (M). If an object is going exactly the speed of sound, it’s going Mach 1 (because v = a).

Since Mach number (M) is v / a, we can plug it into the formula from above as 1 / M and use [Andrew]’s calculation shown in the image at the top of the article for a Mach angle (µ) of ~11.7°:

\bf \sin ( \mu ) = \frac{1}{M} \\ \\ M = \frac{1}{\sin(\mu)} \\ \\ M = \frac{1}{\sin(11.7)} \\ \\ M = \frac{1}{0.202787295357} \\ \\ M = 4.9312753949380048

The real question is, did the USPS chose Mach 4.93 as a hint to some secret government postal project? Or, was it simply a 1993 logo designer’s attempt to “capture the ethos of a modern era which continues today”?

Miss Beatrice Shilling Saves The Spitfire

On a bright spring morning in 1940, the Royal Air Force pilot was in the fight of his life. Strapped into his brand new Supermarine Spitfire, he was locked in mortal combat with a Luftwaffe pilot over the English Channel in the opening days of the Battle of Britain. The Spitfire was behind the Messerschmitt and almost within range to unleash a deadly barrage of rounds from the four eight Browning machine guns in the leading edges of the elliptical wings. With the German plane just below the centerline of the gunsight’s crosshairs, the British pilot pushed the Spit’s lollipop stick forward to dive slightly and rake his rounds across the Bf-109. He felt the tug of the harness on his shoulders keeping him in his seat as the nimble fighter pulled a negative-g dive, and he lined up the fatal shot.

But the powerful V-12 Merlin engine sputtered, black smoke trailing along the fuselage as the engine cut out. Without power, the young pilot watched in horror as the three-bladed propeller wound to a stop. With the cold Channel waters looming in his windscreen, there was no time to restart the engine. The pilot bailed out in the nick of time, watching his beautiful plane cartwheel into the water as he floated down to join it, wondering what had just happened.

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3D Printing RC Airplanes That Fly: An Engineer’s Chronicle

In the past, creating accurate replicas of models and fantasy objects was a task left to the most talented of cosplayers. These props need not be functional, though. [Steve Johnstone] takes replica model-building to the next step. He’s designing and building a model airplane that flies, and he’s documenting every step of the way.

Armed with a variety of 3D printing techniques and years of model-building experience, [Steve] is taking the lid off a number of previously undocumented techniques, many of which are especially relevant to the model-builder equipped with a 3D printer in the workshop.

As he continues his video log, [Steve] takes you through each detail, evaluating the quality of both his tools and techniques. How does a Makerbot, a Formlabs, and a Shapeways print stand up against being used in the target application? [Steve] evaluates a number of his turbine prints with a rigorous variable-controlled test setup.

How can we predict the plane’s center-of-gravity before committing to a physical design? [Steve] discusses related design decisions with an in-depth exploration of his CAD design, modeled down to the battery-pack wires. Though he’s not entirely finished, [Steve’s] work serves as a great chance to “dive into the mind of the engineer,” a rare opportunity when we usually discover a project after it’s been sealed from the outside.

3D printing functional parts with hobbyist-grade printers is still a rare sight, though we’ve seen a few pleasant and surprisingly practical components. With some tips from [Steve], we may complete this video journey with a few techniques that bump us out of the “novelty” realm and into a space where we too can start reliably printing functional parts. We’re looking forward to seeing the maiden voyage.

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